Limit theorems for coupled continuous time random walks
成果类型：
Article
署名作者：
Becker-Kern, P; Meerschaert, MM; Scheffler, HP
署名单位：
Dortmund University of Technology; Nevada System of Higher Education (NSHE); University of Nevada Reno
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2004
页码：
730-756
关键词：
摘要：
Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time between jumps are dependent. This leads to an efficient method of computing the limit, and a surprising connection to fractional derivatives.